zero intervals and benefit cost analysis

[david.barton@nina.no]

I tried implementing zero intervals in the Learning Wizard (Hugin 8.0)  for the variable “wtp” (willingness-to-pay for water quality improvement) , using Discretize Manual in the Preprocessor, using the tab-delimited datafile (see attached).

What did I expect as a result?  I expected to see the interval 0-0 in CPT for “wtp”  with zero probability across all parent states (“user_type”, “dist”, “qual”).  As far as I know there are no simulation results for “wtp” exactly equal to zero,  but I still need the interval to appear in the CPT with zero probability (I don’t expect Hugin Wizard to drop intervals without observations, but maybe this happens).

Why do I need this?   Later I manually create the state “none” for the node “qual” to represent ‘water quality improvement is none’.   I then want to attach a 100% probability to a 0-0 interval in “wtp” indicating that there is exactly zero willingness to pay for water quality improvement equals “none”.  Without the 0-0 interval I have to assign an equal probability to the intervals -1000-0 and 0-1000 to capture the idea, but I lose information with a “fuzzy zero” of this kind.

This may sound trivial, but it is a key feature of integrating monetary valuation method results with DPSIR modelling in BBNs, and then conducting cost-benefit analysis of decisions.

Can you help?

Kind Regards,
David

P.S. How do I attach Hugin files to this "topic?"

[Anders L Madsen]

Can you help?

We can try.

1) Explanation.

The zero width interval -feature was introduced to extend the Table generator functionality. We did not consider including this as part of the Learning Wizards. So, the discretization operator in the Learning Wizard simply ignores the zero width interval.

2) Workaround.

Here is a workaround (I assume that you are using the Learning Wizard and not only the EM Learning Wizard):

• do the discretization  and structure learning in Learning Wizard
• leave the Learning Wizard prior to the EM part (parameter estimation)
• manually add the "zero width interval" to the appropriate node
• use the EM learning wizard to perform the parameter estimation on the adjusted model
  

If your are using the EM learning wizard, then the steps should be adjusted accordingly.

As you have no data on zero, then you will probably not learning anything about the relation between the parents for this value. The result will probably be a uniform likelihood.